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Dissolution kinetics at the calcite-water interface
Geochimicaet CosmochimicaActa, Vol. 60, No. 23, pp. 4883-4887, 1996 Copyright© 1996 ElsevierScienceLtd Printed in the USA. All rights reserved 0016-7037/96 $15.00 + .00
Pergamon
P I I S0016-7037(96) 00337-7
LETTER
Dissolution kinetics at the calcite-water interface YONG LIANG, DONALD R. BAER, JAMES M. McCoY, JAMES E. AMONETIE, and JOHN P. LAFEMINA Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA 99352, USA (Received June 24, 1996; accepted in revised form September 18, 1996) A b s t r a c t - - A l t h o u g h many geochemical processes, including mineral dissolution, are controlled by kinetic mechanisms, quantitative descriptions of the reaction kinetics are mostly lacking, principally due to an incomplete understanding of the molecular-scale processes controlling these reactions. In this paper, a combined experimental and theoretical approach involving atomic force microscopy, an analytical terrace-ledge-kink model, and kinetic Monte Carlo computer simulations was used to study the aqueous dissolution kinetics of the calcite (10T4) surface. The study provides a determination of the elementary rates and activation energies associated with dissolution at specific kink sites on the calcite surface. 1. INTRODUCTION
(Dove and Hochella, 1993), largely because suitable techniques were not available. Recent developments, for example, in atomic-force microscopy ( A F M ) (Gratz et al., 1991, 1993; Ohnesorge and Binnig, 1993), ab initio computational chemistry (Gibson and LaFemina, 1996), and surface X-ray diffraction techniques (Qian et al., 1994) now offer the ability to examine the mineral-water interface in sufficient detail to begin to finally unravel the molecular-level processes. Pioneering observations of calcite growth in an aqueous environment were conducted using AFM (Gratz et al., 1993; Dove and Hochella, 1993 ). Use of AFM allows the determination of atomic-scale structural information of calcite surfaces in contact with aqueous solutions (Ohnesorge and Binnig, 1993; Stipp et al., 1994; Liang et al., 1996a) and has been applied to other systems and environments. In this paper, we extend the AFM approach to obtain in situ, "realtime" dissolution information on specific crystallographic sites. We are asking, in effect, how much molecular-level kinetic information can be obtained from AFM images. In what follows, AFM observations of the geometry and orientation of pits on the surface and their growth as a function of time and temperature, combined with an analytical terraceledge-kink (TLK) model and kinetic Monte Carlo (KMC) computer simulations, are used to extract kinetic information for specific kink sites.
Many important geochemical reactions involve mass transfer across the aqueous-mineral interface. Fundamentally, this process depends on molecular-scale interactions of the species comprising the aqueous matrix and the mineral surface. These interactions ultimately combine to yield the interfacial phenomena that are observed and described macroscopically by equilibrium thermodynamics or kinetic rate laws. Any rigorous attempt to understand and control the chemistry of the aqueous-mineral interface, therefore, must include an explicit model of these molecular-scale interactions. Calcite (rhombohedral CaCO3) is abundant in nature and able to adsorb and coprecipitate with metallic cations and oxyanions of environmental and geological interest (White et al., 1995). It also functions as a reservoir that buffers aqueous and atmospheric levels of CO2 (Berner et al., 1983 ). Consequently, the chemistry of the calcite-water interface, and, in particular, the kinetics of mass transfer across this interface, are of great interest to the environmental and geochemical communities. The development of a better understanding of calcite dissolution and nucleation is important to the improvement of macroscopic models of global warming and subsurface contaminant transport. The dissolution of calcite in water has been studied by many experimental methods (e.g., Plummer et al., 1979; Morse, 1983; Sjoberg and Rickard, 1984; Maclnnis and Brantley, 1992; Gratz et al., 1993). With the exception of a few studies on single-crystal calcite (Sjoberg and Rickard, 1984; Maclnnis and Brantley, 1992), most of these studies have focused on the dissolution of powdered specimens in solution, with emphasis on the amounts of dissolved species and the total material transfer from calcite to the solution (e.g., Morse, 1983). Empirical rate laws have been derived from these data (Morse, 1983; Sjoberg and Rickard, 1984; Maclnnis and Brantley, 1992). However, a more fundamental approach to the study of calcite dissolution, in which the effects of structure and surface morphology are explicitly considered at the molecular scale, has not been reported
2. EXPERIMENTAL METHOD
The microscope (Nanoscope HI, Digital Instruments, California, USA) is capable of examining specimens immersed in flowing solutions at temperatures between 22 and 50°C and has a solution cell volume of ~20 #L. The solution flow rate was controlled by an electrical syringe pump. The temperature variation was accomplished by pumping the warm solution into the AFM cell and by using a thermal-electronic device placed underneath the sample. The temperature was monitored by a type-k thermocouple which was in contact with the sample surface exposed to the solution. Iceland spar single-crystal calcite surfaces were prepared by cleaving along the natural (10T4) cleavage plane. The dissolving solution consisted of purified deionized water adjusted to an initial pH of 9 using NaOH and was used immediately after the solution preparation. In order 4883
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Y. Liang et al.
to focus on the effects of surface reactions rather than solution diffusion processes, our experiments were performed under high flow-rate conditions (2.5 #L s -~ or greater) where the effect of diffusion on the kinetics of shallow surface features can be demonstrated to be negligible (Liang et al., 1996b). More complete experimental details are described elsewhere (Liang et al.. 1996a,b). 3. RESULTS AND DISCUSSION Upon exposure to the solution, the calcite surface dissolves by the creation of rhombic pits and the retreat of steps. Two types of pits are created: shallow pits initiated by point defects and/or impurities, and deep pits initiated by dislocations (Gilman et al., 1958; Liang et al., 1996b). Figure 1 shows an A F M image of a surface that was exposed to the solution for 4 min. The surface had been step-free over an area of 12 # m x 12 # m before solution exposure. The depths of these pits are mostly one atomic-layer ( ~0.3 nm) and the steps orient along either the (481) or the {441 ) direction. The rhombic pit shape reflects the symmetry of the calcite crystal lattice and the fixed step orientations suggest a preferential dissolution along these two directions. Irregularly shaped pits and wavy steps are also evident in Fig. 1. These were mostly caused by the merging of two pits, or by a pit and a step. All the shallow pits observed occurred frequently but were short-lived. The integrity of the rhombic pits typically lasted a few minutes before the pits merged with other features on the surface. In contrast to shallow pits, deeper pits occurred less frequently (density of ~103 cm 2), but came to dominate the surface topography after a few hours. Two such pits, one at an early stage of development and the other somewhat later when vertical pit growth appears to have stopped at a depth of - 4 0 layers, are shown in Fig. 2. In addition to their greater depth, deep pits were also distinguished by their skewed shape among different layers. In the early stages of development, this is shown by the occurrence of both narrow and wide terraces on opposite sides of the pit; while at later stages, it is shown by the presence of different slopes. In contrast to the shallow pits, the deep pits continuously deep-
FIG. 1. A 12 #m X 12 ¢zm AFM image of the cleaved CaCO3(1014) surface after 4 min solution exposure. As a result of dissolution, many shallow, rhombic pits formed at the surface.
FIG. 2. (a) A 2 #m × 2 #m AFM image showing an early stage of a deep pit (five-layer depth) at the CaCO3(10i4) surface. The skewed shape demonstrates the two step velocities, vf and v~, involved during the pit growth. (b) A 15 #m × 15/~m image showing the slopes and flat bottom of an inverted deep pit. The depth scale is enhanced by a factor of 1000 ( 15 nm from black to white) relative to the lateral scale.
ened and widened. As a result, they covered most of the surface area and became the permanent features on the surface typically after a few hours. Thus, dissolution follows a "layer-by-layer" removal fashion via creation and annihilation of shallow pits at early stages. Eventually the surface becomes dominated by a significantly more three-dimensional topography, although dissolution is still controlled by the retreat of single-layer steps. Similar changes in morphology have been observed using surface X-ray diffraction (N. C. Sturchio and R. P. Chiarello, pers. commun., 1996). Having observed the different types of pits present on the surface, what molecular-scale information can be obtained? The answer is a great deal. Although many details will not be presented here, the geometry and morphology of the pits, the rates at which they grow, and the temperature dependence of the pit growth all provide important information for modeling the dissolution of calcite.
Dissolution kinetics of calcite surfaces The straight steps of the pits allow a velocity of opening to be measured. Figure 3 shows two time-lapse images that demonstrate the growth of a shallow pit on the surface. The integrity of the pit was maintained for approximately 5 min before the pit vanished when it collided with other surface steps. By plotting the pit width as a function of time, the summed velocity of the two parallel steps retreating in opposite directions can be determined. From many measurements on pits having different sizes, the average summed step velocity was found to be a constant of 4.9 ___ 0.7 nm s -~ at room temperature. This value is similar to the 5.4 nm s -~ observed for macroscopic pits using optical microscopy (Maclnnis and Branfley, 1992). Detailed observations indicate that the rate of pit growth, over a wide size range (150 nm to 20 #m), is independent of pit size. The constant step velocities and straight step morphology have important implications for the nature of the calcite dissolution process. A straight step morphology is obtained when the rate of single-kink retreat, Rk, is much greater than the rate of double-kink nucleation, Rkk (these
4885
vt
vt FIG. 4. A schematic showing two different double-kink sites and three different single-kink sites at different step edges of a pit. The two different double-kink sites are caused by the two inequivalent steps while the three different single-kink sites are caused by three different intersections of the two equivalent or inequivalent steps. The shaded area is the bottom of the pit.
FIG. 3. Two time-lapse AFM images showing the growth of a surface pit as a result of dissolution. The time span between (a) and (b) is 243 s.
rates are illustrated in Fig. 4). A constant velocity occurs when the average nucleation time of a double-kink equals the average annihilation time of two adjacent double-kink sites. Thus, the straight steps and constant summed velocity are an indication of a correlation among molecular-level processes. This "kink-kink annihilation" process was initially used to explain the motion of dislocation lines (Hirth and Lothe, 1982) and has been applied to the dissolution of calcite (Liang et al., 1996b). As will be discussed later, the measured velocities and their temperature variation can be used to estimate the rates Rk and Rkk and the related effective activation energies. For the deep pits in Fig. 2, the difference in the terrace width is caused either by two different step velocities during the pit growth, or by the inclination of the dislocation line to the surface so that the pit initiates at different lateral positions in different layers. We have concluded that the difference in the terrace width is predominantly caused by the difference in step velocity for the following two reasons. First, the anisotropic velocities were also observed for the shallow pits when a stable surface feature allowed an absolute reference point on the surface. Second, if the difference in the terrace width is caused by the inclination of the dislocation line, the angle between the dislocation line and the surface has to be as small as 0.8 °. A dislocation with such a small angle to the surface is unstable under the image force (Hirth and Lothe, 1982). Consequently, the ratio of the two terrace widths equals the ratio of the two step velocities; i.e., there exist a fast velocity, v f, for the wide terraces and a slow velocity, vs, for the narrow terraces. Such an anisotropy
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Y. Liang et al.
in velocity is also manifested in the different slopes of the sides of deep pits. The fiat bottom and enclosed (nonspiral) steps of the deep pits also seem to indicate that screw dislocations, the primary nucleus for growth (Gratz et al., 1993; Dove and Hochella, 1993), are energetically less favorable for calcite dissolution. Skewed pit shapes have also been observed for much larger pits using optical microscopy and the cause of the anisotropy suggested as being likely a difference in step velocities (Maclnnis and Brantley, 1992). From a series of measurements on deep pits having different sizes, the average ratio of the two terrace widths and, thus, the ratio of the two step velocities v f l v ~ , was found to be a constant of 2.3 _ 0.2 at room temperature. From the ratio and sum of the two step velocities, we can determine the two different single-layer step velocities: vf = 3.4 nm s ' and vs = 1.5 n m s - 1 . For the CaCO3 (10]4) surface, the (48]-) and (441) directions are crystallographically equivalent. However, there are two inequivalent steps possible along each direction. The surface pits orient in a way such that the equivalent steps are adjacent but the inequivalent steps are parallel to each other. For one type of step, the step-edge atoms on the upper terrace overhang and an acute angle of 78 ° is formed, while at the opposite side of the pit, the step-edge atoms on the upper terrace underhang and an obtuse angle of 102° is formed. Such a difference in atomic step structure results in different step energies and steric effects affecting dissolution at the steps. By comparing the step directions with the crystallographic structure of calcite, the obtuse step was found to correspond to the fast step. Based upon the different angles exposed, there are two different double-kink sites with rates R~ and R~ for obtuse and acute steps, respectively, and three different single-kink sites with rates R~f, R~?, and R~ s (where f and s relate to the angles, obtuse or acute, respectively, of the sides of the kink), as marked in Fig. 4. By incorporating these features into the "kink-kink annihilation" model, the step velocities can be directly related to the elementary rates of the double kinks and single kinks (Liang et al., 1996b): a [ R k fk ( R k f f + R~)]I/~
(la)
v~ = a [ R ~ , k ( R ~ ~ + Rf~)] w2
(lb)
vf
=
where a is the distance between adjacent sites. Thus, Eqns. la and b show that Ve and v~ depend explicitly on the sitespecific rates. The summed step velocity as a function of temperature can be measured using time-lapse AFM images (Liang et al., 1996b). By assuming that the step velocities have an Arrhenius behavior (i.e., v = C e x p ( - E / k T ) , where E is the effective activation energy and C is the entropy-related prefactor), the relationship between the summed velocity and an effective activation energy can be extracted. The difference between the fast and slow velocities is likely to be produced by both a difference in the prefactors and a difference in the energies associated with the two types of steps. However, only the two limiting cases are considered here. If the differences are attributed solely to differences in prefactor, the relevant activation energy obtained is 0.60 eV and the prefactors are C, = 1.9 × 10 I° n m s -~ and Cf = 4.3 x 10 to nm s-~. If the prefactors are assumed to be identical
3
I
I
I °
,-'-,
I ~
°
2.5
t~
I,,g ~I,,g "1"
2
1.5
÷
1
0.5 3.15
I
I
I
3.2
3.25
3.3
looorr
('VK)
I 3,35
3,4
FIG. 5. An Arrhenius plot of the summed step-velocityat different temperatures.
then there is an energy difference between the two steps of Es - Ef = 22 _ 5 meV and the absolute energies are Ef = 0.59 eV and E~ = 0.61 eV, while the prefactor is 3.3 × 101° nm s ~. The plot of the summed step velocity as a function of temperature in Fig. 5 uses the constant prefactor assumption. Although the anisotropy in step velocity is assumed to originate from entirely different causes, both methods yield essentially the same effective activation energy. Information related to the five different kinks shown in Fig. 4 has been obtained using both TLK and KMC models of dissolution. The KMC model is based on the solid-onsolid (SOS) model (Weeks and Gilmer, 1979). The details of the TLK and KMC models are described elsewhere (Hirth and Lothe, 1982; Weeks and Gilmer, 1979; Liang and Baer, 1996; McCoy and LaFemina, 1996). In these models, the rates are assumed to have an Arrhenius behavior. An energy is associated with nearest-neighbor bond directions for each type of site on a step. These energies are assumed to be altered by the obtuse or acute nature of the angles between the site and the underlayer. Two in-plane site-site interaction energies e* and e* are associated with the obtuse and acute geometries, respectively, in both the TLK and KMC models. By fitting the KMC model to the experimental results, both the site-site interaction energies and the elementary rates occurring in Eqn. 1 can be estimated. The site-site interaction energies obtained in this manner agree very well with those obtained by the TLK model. Values obtained for the elementary rates (Table 1) vary significantly among the different kink sites and thus provide a molecular-scale explanation for the observed anisotropy in step velocity. Measurements of activation energies of calcite dissolution have not been common and it is important to compare the current results to energies obtained by other techniques. Sjoberg and Rickard (1984) reported an apparent activation energy of 0.48 _+ 0.04 eV for bulk dissolution in the surfacereaction-controlled regime. Maclnnis and Brantley (1992) reported apparent activation energies of 0.61 _+ 0.12 eV for
Dissolution kinetics of calcite surfaces TABLE 1. Summary of the elementary rates occurring in the TLK model obtained from fitting the KMC model to the experimental data. The rates are obtained from the equation R = A exp {-[½(e* + e)*) + nse* + nre~']/kT} at T = 300K, usingA = 5.22 × l0 l°s 1 e, = 0.181eVandE~ = 0.159eV. l~te
n,
nI
V~l.ue(s-t )
.R~,~
2
1
0.129
Rh/t,
1
2
0.301
R~,"
2
0
6o.3
/~k'
1
1
141.2
/~
0
2
330.6
bulk dissolution and of 0.38 __+ 0.03 eV for widening of macroscopic deep pits. The effective activation energy of the shallow, microscopic pit widening (summed step velocity) obtained from the current experiment is 0.60 _+ 0.15 eV. W e do not have an obvious explanation for the significant difference between our result for single-layer, microscopic pits (0.60 eV) and that obtained for the macroscopic pits (0.38 e V ) . However, such difference could result from faceting or changes in solution conditions (such as nonnegligible effects of diffusion processes close to the pit bottom) within the deeper pits. All our observations show that dissolution predominantly occurs at step edges. Although the appearance of the surface may be dominated by the deep pits, dissolution proceeds at single-layer step edges (layer-by-layer removal). Thus, the velocities observed in the growth of single-layer pits should control the general dissolution process. When a steady surface morphology is achieved (MacInnis and Brantley, 1992), the rate of layer removal, Rlayer, is proportional to the step density; i.e., Rlayer = ~.(1)f q- Vs)/2, where k is the average step density. In this model, the dissolution activation energy is the same as that for the growth of the shallow pits, providing an explanation of the agreement between the apparent activation energy for bulk dissolution (Sjoberg and Rickard, 1984; Maclnnis and Brantley, 1992) and that observed for the shallow pits. The layer-by-layer observations are also consistent with the weak dependence of dissolution rate on dislocation density (Schott et al., 1989). The site-specific details of calcite dissolution reported here demonstrate an important use of AFM, in conjunction with T L K and KMC models of dissolution, to unravel molecularscale information. These results have implications in two directions. First, the study identifies additional questions related to dissolution which may be addressed using both experimental and theoretical methods, e.g., the difference in the activation energies between anion and cation sites and their related transition states during dissolution, and questions regarding the active sites during the production and turn off of deep pits (Maclnnis and Brantley, 1992). Second, they provide microscopic kinetics to be included in macroscopic models of dissolution. Although the current work has been conducted on dissolution of a relatively simple mineral surface and solution, the methods used in this paper can be extended to study dissolution and growth of other mineral phases in more complex solutions. This approach presents many exciting possibilities for elucidating the kinetics of processes occurring at solid-liquid interfaces.
4887
Acknowledgments This work was supported by the Division of Geosciences, Office of Basic Energy Science, US Department of Energy. PNNL is a multiprogram national laboratory operated for the Department of Energy by Battelle Memorial Institute under contract DE-AC06-76RLO1830. We acknowledge valuable discussions with Drs. J. P. Hirth, B. D. Kay, and S. A. Joyce. Editorial handling: J. D. Macdougall REFERENCES
Bemer R. A., Lasaga A. C., and Garrels R. M. (1983) The carbonatesilicate geochemical cycle and its effect on atmospheric carbon dioxide over the past 100 million years. Amer. J. Sci. 283, 641-683. Dove P.M. and Hochella M.F., Jr. (1993) Calcite precipitation mechanisms and inhibition by orthophosphate: In situ observation by Scanning Force Microscopy. Geochim. Cosmochim. Acta 57, 705-714. Hirth J. P. and Lothe J. (1982) Theory of Dislocations. McGrawHill. Gibson A. S. and LaFemina J. P. (1996) Structure of mineral surfaces. In Physics and Chemistry of Mineral Surfaces (ed. P. V. Brady), pp. 1-62. CRC. Gilman J. J., Johnston W. G., and Sears G. W. (1958) Dislocation etch pit formation in lithium fluoride. J. AppL Phys. 29, 747-754. Gratz A. J., Manne S., and Hansma P. K. ( 1991 ) Atomic force microscopy of atomic-scale ledges and etch pits formed during dissolution of quartz. Science 251, 1343-1346. Gratz A. J., Hillner P. E., and Hansma P. K. (1993) Step dynamics and spiral growth on calcite. Geochim. Cosmochim. Acta 57, 491495. Liang Y. and Baer D.R. (1996) Anisotropic dissolution at the CaCO3(10T4)-water interface. S u ~ Sci. (in press). Liang Y., Lea A. S., Baer D. R., and Engelhard M. H. (1996a) Structure of the cleaved CaCO3(1014) surface in an aqueous environment. S u ~ Sci. 351, 172-182. Liang Y., Baer D. R., McCoy J. M., and LaFemina J. P. (1996b) Interplay between step velocity and morphology during the dissolution of CaCO3 surface. J. Vac. Sci. Technol. A 14, 1368-1375. Maclnnis I. N. and Brantley S. L. (1992) The role of dislocations and surface morphology in calcite dissolution. Geochim. Cosmochim. Acta 56, 1113-1126. McCoy J. M. and LaFemina J. P. (1996) Kinetic Monte Carlo investigation of pit formation at the CaCO3(1014) surface-water interface. Surf. Sci. (in press) Morse J.W. (1983) The kinetics of calcium carbonate dissolution and precipitation. In Carbonates: Mineralogy and Chemistry (ed. R. J. Reeder) ; Rev. Mineral. 11, pp. 227-264a. Ohnesorge F. and Binnig G. (1993) True atomic resolution by atomic force microscopy through repulsive and attractive forces. Science 260, 1451-1456. Plummer L. N., Parkhurst D. L., and Wigley T. M. L. (1979) Critical review of the kinetics of calcite dissolution and precipitation. In Chemical Modeling in Aqueous System; Amer. Chem. Symp. Ser. No. 93, pp. 537-573. Qian Y., Sturchio N. C., Chiarello R.P., Lyman P. F., Lee T.-L., and Bedzyk J. (1994) Lattice location of trace elements within minerals and at their surfaces with x-ray standing waves. Science 265, 1555-1557. Schott J., Brantley S., Crerar D., Guy C., Borcsik M., and Willaime C. (1989) Dissolution kinetics of strained calcite. Geochim. Cosmochim. Acta 53, 373-382. Sjoberg E. L. and Rickard D. T. (1984) Temperature dependence of calcite dissolution kinetics between 1 and 62°C at pH 2.7 to 8.4 in aqueous solutions. Geochim. Cosmochim. Acta 48, 485-493. Stipp S. L. S., Eggleston C.M., and Nielsen B. S. (1994) Calcite surface structure observed at microtopographic and molecular scales with atomic force microscopy (AFM). Geochim. Cosmochim. Acta 58, 3023-3033. Weeks J. D. and Gilmer G. H. (1979) Dynamics of Crystal growth. Adv. Chem. Phys. 40, 157-228. White W. B., Culver D. C., Herman J. S., Kane T. C., and Mylroie J. E. (1995) Karst lands. Amer. Scientist 83, 450-459.
Pergamon
P I I S0016-7037(96) 00337-7
LETTER
Dissolution kinetics at the calcite-water interface YONG LIANG, DONALD R. BAER, JAMES M. McCoY, JAMES E. AMONETIE, and JOHN P. LAFEMINA Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA 99352, USA (Received June 24, 1996; accepted in revised form September 18, 1996) A b s t r a c t - - A l t h o u g h many geochemical processes, including mineral dissolution, are controlled by kinetic mechanisms, quantitative descriptions of the reaction kinetics are mostly lacking, principally due to an incomplete understanding of the molecular-scale processes controlling these reactions. In this paper, a combined experimental and theoretical approach involving atomic force microscopy, an analytical terrace-ledge-kink model, and kinetic Monte Carlo computer simulations was used to study the aqueous dissolution kinetics of the calcite (10T4) surface. The study provides a determination of the elementary rates and activation energies associated with dissolution at specific kink sites on the calcite surface. 1. INTRODUCTION
(Dove and Hochella, 1993), largely because suitable techniques were not available. Recent developments, for example, in atomic-force microscopy ( A F M ) (Gratz et al., 1991, 1993; Ohnesorge and Binnig, 1993), ab initio computational chemistry (Gibson and LaFemina, 1996), and surface X-ray diffraction techniques (Qian et al., 1994) now offer the ability to examine the mineral-water interface in sufficient detail to begin to finally unravel the molecular-level processes. Pioneering observations of calcite growth in an aqueous environment were conducted using AFM (Gratz et al., 1993; Dove and Hochella, 1993 ). Use of AFM allows the determination of atomic-scale structural information of calcite surfaces in contact with aqueous solutions (Ohnesorge and Binnig, 1993; Stipp et al., 1994; Liang et al., 1996a) and has been applied to other systems and environments. In this paper, we extend the AFM approach to obtain in situ, "realtime" dissolution information on specific crystallographic sites. We are asking, in effect, how much molecular-level kinetic information can be obtained from AFM images. In what follows, AFM observations of the geometry and orientation of pits on the surface and their growth as a function of time and temperature, combined with an analytical terraceledge-kink (TLK) model and kinetic Monte Carlo (KMC) computer simulations, are used to extract kinetic information for specific kink sites.
Many important geochemical reactions involve mass transfer across the aqueous-mineral interface. Fundamentally, this process depends on molecular-scale interactions of the species comprising the aqueous matrix and the mineral surface. These interactions ultimately combine to yield the interfacial phenomena that are observed and described macroscopically by equilibrium thermodynamics or kinetic rate laws. Any rigorous attempt to understand and control the chemistry of the aqueous-mineral interface, therefore, must include an explicit model of these molecular-scale interactions. Calcite (rhombohedral CaCO3) is abundant in nature and able to adsorb and coprecipitate with metallic cations and oxyanions of environmental and geological interest (White et al., 1995). It also functions as a reservoir that buffers aqueous and atmospheric levels of CO2 (Berner et al., 1983 ). Consequently, the chemistry of the calcite-water interface, and, in particular, the kinetics of mass transfer across this interface, are of great interest to the environmental and geochemical communities. The development of a better understanding of calcite dissolution and nucleation is important to the improvement of macroscopic models of global warming and subsurface contaminant transport. The dissolution of calcite in water has been studied by many experimental methods (e.g., Plummer et al., 1979; Morse, 1983; Sjoberg and Rickard, 1984; Maclnnis and Brantley, 1992; Gratz et al., 1993). With the exception of a few studies on single-crystal calcite (Sjoberg and Rickard, 1984; Maclnnis and Brantley, 1992), most of these studies have focused on the dissolution of powdered specimens in solution, with emphasis on the amounts of dissolved species and the total material transfer from calcite to the solution (e.g., Morse, 1983). Empirical rate laws have been derived from these data (Morse, 1983; Sjoberg and Rickard, 1984; Maclnnis and Brantley, 1992). However, a more fundamental approach to the study of calcite dissolution, in which the effects of structure and surface morphology are explicitly considered at the molecular scale, has not been reported
2. EXPERIMENTAL METHOD
The microscope (Nanoscope HI, Digital Instruments, California, USA) is capable of examining specimens immersed in flowing solutions at temperatures between 22 and 50°C and has a solution cell volume of ~20 #L. The solution flow rate was controlled by an electrical syringe pump. The temperature variation was accomplished by pumping the warm solution into the AFM cell and by using a thermal-electronic device placed underneath the sample. The temperature was monitored by a type-k thermocouple which was in contact with the sample surface exposed to the solution. Iceland spar single-crystal calcite surfaces were prepared by cleaving along the natural (10T4) cleavage plane. The dissolving solution consisted of purified deionized water adjusted to an initial pH of 9 using NaOH and was used immediately after the solution preparation. In order 4883
4884
Y. Liang et al.
to focus on the effects of surface reactions rather than solution diffusion processes, our experiments were performed under high flow-rate conditions (2.5 #L s -~ or greater) where the effect of diffusion on the kinetics of shallow surface features can be demonstrated to be negligible (Liang et al., 1996b). More complete experimental details are described elsewhere (Liang et al.. 1996a,b). 3. RESULTS AND DISCUSSION Upon exposure to the solution, the calcite surface dissolves by the creation of rhombic pits and the retreat of steps. Two types of pits are created: shallow pits initiated by point defects and/or impurities, and deep pits initiated by dislocations (Gilman et al., 1958; Liang et al., 1996b). Figure 1 shows an A F M image of a surface that was exposed to the solution for 4 min. The surface had been step-free over an area of 12 # m x 12 # m before solution exposure. The depths of these pits are mostly one atomic-layer ( ~0.3 nm) and the steps orient along either the (481) or the {441 ) direction. The rhombic pit shape reflects the symmetry of the calcite crystal lattice and the fixed step orientations suggest a preferential dissolution along these two directions. Irregularly shaped pits and wavy steps are also evident in Fig. 1. These were mostly caused by the merging of two pits, or by a pit and a step. All the shallow pits observed occurred frequently but were short-lived. The integrity of the rhombic pits typically lasted a few minutes before the pits merged with other features on the surface. In contrast to shallow pits, deeper pits occurred less frequently (density of ~103 cm 2), but came to dominate the surface topography after a few hours. Two such pits, one at an early stage of development and the other somewhat later when vertical pit growth appears to have stopped at a depth of - 4 0 layers, are shown in Fig. 2. In addition to their greater depth, deep pits were also distinguished by their skewed shape among different layers. In the early stages of development, this is shown by the occurrence of both narrow and wide terraces on opposite sides of the pit; while at later stages, it is shown by the presence of different slopes. In contrast to the shallow pits, the deep pits continuously deep-
FIG. 1. A 12 #m X 12 ¢zm AFM image of the cleaved CaCO3(1014) surface after 4 min solution exposure. As a result of dissolution, many shallow, rhombic pits formed at the surface.
FIG. 2. (a) A 2 #m × 2 #m AFM image showing an early stage of a deep pit (five-layer depth) at the CaCO3(10i4) surface. The skewed shape demonstrates the two step velocities, vf and v~, involved during the pit growth. (b) A 15 #m × 15/~m image showing the slopes and flat bottom of an inverted deep pit. The depth scale is enhanced by a factor of 1000 ( 15 nm from black to white) relative to the lateral scale.
ened and widened. As a result, they covered most of the surface area and became the permanent features on the surface typically after a few hours. Thus, dissolution follows a "layer-by-layer" removal fashion via creation and annihilation of shallow pits at early stages. Eventually the surface becomes dominated by a significantly more three-dimensional topography, although dissolution is still controlled by the retreat of single-layer steps. Similar changes in morphology have been observed using surface X-ray diffraction (N. C. Sturchio and R. P. Chiarello, pers. commun., 1996). Having observed the different types of pits present on the surface, what molecular-scale information can be obtained? The answer is a great deal. Although many details will not be presented here, the geometry and morphology of the pits, the rates at which they grow, and the temperature dependence of the pit growth all provide important information for modeling the dissolution of calcite.
Dissolution kinetics of calcite surfaces The straight steps of the pits allow a velocity of opening to be measured. Figure 3 shows two time-lapse images that demonstrate the growth of a shallow pit on the surface. The integrity of the pit was maintained for approximately 5 min before the pit vanished when it collided with other surface steps. By plotting the pit width as a function of time, the summed velocity of the two parallel steps retreating in opposite directions can be determined. From many measurements on pits having different sizes, the average summed step velocity was found to be a constant of 4.9 ___ 0.7 nm s -~ at room temperature. This value is similar to the 5.4 nm s -~ observed for macroscopic pits using optical microscopy (Maclnnis and Branfley, 1992). Detailed observations indicate that the rate of pit growth, over a wide size range (150 nm to 20 #m), is independent of pit size. The constant step velocities and straight step morphology have important implications for the nature of the calcite dissolution process. A straight step morphology is obtained when the rate of single-kink retreat, Rk, is much greater than the rate of double-kink nucleation, Rkk (these
4885
vt
vt FIG. 4. A schematic showing two different double-kink sites and three different single-kink sites at different step edges of a pit. The two different double-kink sites are caused by the two inequivalent steps while the three different single-kink sites are caused by three different intersections of the two equivalent or inequivalent steps. The shaded area is the bottom of the pit.
FIG. 3. Two time-lapse AFM images showing the growth of a surface pit as a result of dissolution. The time span between (a) and (b) is 243 s.
rates are illustrated in Fig. 4). A constant velocity occurs when the average nucleation time of a double-kink equals the average annihilation time of two adjacent double-kink sites. Thus, the straight steps and constant summed velocity are an indication of a correlation among molecular-level processes. This "kink-kink annihilation" process was initially used to explain the motion of dislocation lines (Hirth and Lothe, 1982) and has been applied to the dissolution of calcite (Liang et al., 1996b). As will be discussed later, the measured velocities and their temperature variation can be used to estimate the rates Rk and Rkk and the related effective activation energies. For the deep pits in Fig. 2, the difference in the terrace width is caused either by two different step velocities during the pit growth, or by the inclination of the dislocation line to the surface so that the pit initiates at different lateral positions in different layers. We have concluded that the difference in the terrace width is predominantly caused by the difference in step velocity for the following two reasons. First, the anisotropic velocities were also observed for the shallow pits when a stable surface feature allowed an absolute reference point on the surface. Second, if the difference in the terrace width is caused by the inclination of the dislocation line, the angle between the dislocation line and the surface has to be as small as 0.8 °. A dislocation with such a small angle to the surface is unstable under the image force (Hirth and Lothe, 1982). Consequently, the ratio of the two terrace widths equals the ratio of the two step velocities; i.e., there exist a fast velocity, v f, for the wide terraces and a slow velocity, vs, for the narrow terraces. Such an anisotropy
4886
Y. Liang et al.
in velocity is also manifested in the different slopes of the sides of deep pits. The fiat bottom and enclosed (nonspiral) steps of the deep pits also seem to indicate that screw dislocations, the primary nucleus for growth (Gratz et al., 1993; Dove and Hochella, 1993), are energetically less favorable for calcite dissolution. Skewed pit shapes have also been observed for much larger pits using optical microscopy and the cause of the anisotropy suggested as being likely a difference in step velocities (Maclnnis and Brantley, 1992). From a series of measurements on deep pits having different sizes, the average ratio of the two terrace widths and, thus, the ratio of the two step velocities v f l v ~ , was found to be a constant of 2.3 _ 0.2 at room temperature. From the ratio and sum of the two step velocities, we can determine the two different single-layer step velocities: vf = 3.4 nm s ' and vs = 1.5 n m s - 1 . For the CaCO3 (10]4) surface, the (48]-) and (441) directions are crystallographically equivalent. However, there are two inequivalent steps possible along each direction. The surface pits orient in a way such that the equivalent steps are adjacent but the inequivalent steps are parallel to each other. For one type of step, the step-edge atoms on the upper terrace overhang and an acute angle of 78 ° is formed, while at the opposite side of the pit, the step-edge atoms on the upper terrace underhang and an obtuse angle of 102° is formed. Such a difference in atomic step structure results in different step energies and steric effects affecting dissolution at the steps. By comparing the step directions with the crystallographic structure of calcite, the obtuse step was found to correspond to the fast step. Based upon the different angles exposed, there are two different double-kink sites with rates R~ and R~ for obtuse and acute steps, respectively, and three different single-kink sites with rates R~f, R~?, and R~ s (where f and s relate to the angles, obtuse or acute, respectively, of the sides of the kink), as marked in Fig. 4. By incorporating these features into the "kink-kink annihilation" model, the step velocities can be directly related to the elementary rates of the double kinks and single kinks (Liang et al., 1996b): a [ R k fk ( R k f f + R~)]I/~
(la)
v~ = a [ R ~ , k ( R ~ ~ + Rf~)] w2
(lb)
vf
=
where a is the distance between adjacent sites. Thus, Eqns. la and b show that Ve and v~ depend explicitly on the sitespecific rates. The summed step velocity as a function of temperature can be measured using time-lapse AFM images (Liang et al., 1996b). By assuming that the step velocities have an Arrhenius behavior (i.e., v = C e x p ( - E / k T ) , where E is the effective activation energy and C is the entropy-related prefactor), the relationship between the summed velocity and an effective activation energy can be extracted. The difference between the fast and slow velocities is likely to be produced by both a difference in the prefactors and a difference in the energies associated with the two types of steps. However, only the two limiting cases are considered here. If the differences are attributed solely to differences in prefactor, the relevant activation energy obtained is 0.60 eV and the prefactors are C, = 1.9 × 10 I° n m s -~ and Cf = 4.3 x 10 to nm s-~. If the prefactors are assumed to be identical
3
I
I
I °
,-'-,
I ~
°
2.5
t~
I,,g ~I,,g "1"
2
1.5
÷
1
0.5 3.15
I
I
I
3.2
3.25
3.3
looorr
('VK)
I 3,35
3,4
FIG. 5. An Arrhenius plot of the summed step-velocityat different temperatures.
then there is an energy difference between the two steps of Es - Ef = 22 _ 5 meV and the absolute energies are Ef = 0.59 eV and E~ = 0.61 eV, while the prefactor is 3.3 × 101° nm s ~. The plot of the summed step velocity as a function of temperature in Fig. 5 uses the constant prefactor assumption. Although the anisotropy in step velocity is assumed to originate from entirely different causes, both methods yield essentially the same effective activation energy. Information related to the five different kinks shown in Fig. 4 has been obtained using both TLK and KMC models of dissolution. The KMC model is based on the solid-onsolid (SOS) model (Weeks and Gilmer, 1979). The details of the TLK and KMC models are described elsewhere (Hirth and Lothe, 1982; Weeks and Gilmer, 1979; Liang and Baer, 1996; McCoy and LaFemina, 1996). In these models, the rates are assumed to have an Arrhenius behavior. An energy is associated with nearest-neighbor bond directions for each type of site on a step. These energies are assumed to be altered by the obtuse or acute nature of the angles between the site and the underlayer. Two in-plane site-site interaction energies e* and e* are associated with the obtuse and acute geometries, respectively, in both the TLK and KMC models. By fitting the KMC model to the experimental results, both the site-site interaction energies and the elementary rates occurring in Eqn. 1 can be estimated. The site-site interaction energies obtained in this manner agree very well with those obtained by the TLK model. Values obtained for the elementary rates (Table 1) vary significantly among the different kink sites and thus provide a molecular-scale explanation for the observed anisotropy in step velocity. Measurements of activation energies of calcite dissolution have not been common and it is important to compare the current results to energies obtained by other techniques. Sjoberg and Rickard (1984) reported an apparent activation energy of 0.48 _+ 0.04 eV for bulk dissolution in the surfacereaction-controlled regime. Maclnnis and Brantley (1992) reported apparent activation energies of 0.61 _+ 0.12 eV for
Dissolution kinetics of calcite surfaces TABLE 1. Summary of the elementary rates occurring in the TLK model obtained from fitting the KMC model to the experimental data. The rates are obtained from the equation R = A exp {-[½(e* + e)*) + nse* + nre~']/kT} at T = 300K, usingA = 5.22 × l0 l°s 1 e, = 0.181eVandE~ = 0.159eV. l~te
n,
nI
V~l.ue(s-t )
.R~,~
2
1
0.129
Rh/t,
1
2
0.301
R~,"
2
0
6o.3
/~k'
1
1
141.2
/~
0
2
330.6
bulk dissolution and of 0.38 __+ 0.03 eV for widening of macroscopic deep pits. The effective activation energy of the shallow, microscopic pit widening (summed step velocity) obtained from the current experiment is 0.60 _+ 0.15 eV. W e do not have an obvious explanation for the significant difference between our result for single-layer, microscopic pits (0.60 eV) and that obtained for the macroscopic pits (0.38 e V ) . However, such difference could result from faceting or changes in solution conditions (such as nonnegligible effects of diffusion processes close to the pit bottom) within the deeper pits. All our observations show that dissolution predominantly occurs at step edges. Although the appearance of the surface may be dominated by the deep pits, dissolution proceeds at single-layer step edges (layer-by-layer removal). Thus, the velocities observed in the growth of single-layer pits should control the general dissolution process. When a steady surface morphology is achieved (MacInnis and Brantley, 1992), the rate of layer removal, Rlayer, is proportional to the step density; i.e., Rlayer = ~.(1)f q- Vs)/2, where k is the average step density. In this model, the dissolution activation energy is the same as that for the growth of the shallow pits, providing an explanation of the agreement between the apparent activation energy for bulk dissolution (Sjoberg and Rickard, 1984; Maclnnis and Brantley, 1992) and that observed for the shallow pits. The layer-by-layer observations are also consistent with the weak dependence of dissolution rate on dislocation density (Schott et al., 1989). The site-specific details of calcite dissolution reported here demonstrate an important use of AFM, in conjunction with T L K and KMC models of dissolution, to unravel molecularscale information. These results have implications in two directions. First, the study identifies additional questions related to dissolution which may be addressed using both experimental and theoretical methods, e.g., the difference in the activation energies between anion and cation sites and their related transition states during dissolution, and questions regarding the active sites during the production and turn off of deep pits (Maclnnis and Brantley, 1992). Second, they provide microscopic kinetics to be included in macroscopic models of dissolution. Although the current work has been conducted on dissolution of a relatively simple mineral surface and solution, the methods used in this paper can be extended to study dissolution and growth of other mineral phases in more complex solutions. This approach presents many exciting possibilities for elucidating the kinetics of processes occurring at solid-liquid interfaces.
4887
Acknowledgments This work was supported by the Division of Geosciences, Office of Basic Energy Science, US Department of Energy. PNNL is a multiprogram national laboratory operated for the Department of Energy by Battelle Memorial Institute under contract DE-AC06-76RLO1830. We acknowledge valuable discussions with Drs. J. P. Hirth, B. D. Kay, and S. A. Joyce. Editorial handling: J. D. Macdougall REFERENCES
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